Infrared stellar photometry from the Two Micron All-Sky Survey (2MASS) and spectral line imaging observations of 12CO and 13CO J = 1–0 line emission from the Five College Radio Astronomy Observatory (FCRAO) 14-m telescope are analysed to assess the variation of the CO abundance with physical conditions throughout the Orion A and Orion B molecular clouds. Three distinct Av regimes are identified in which the ratio between the 13CO column density and visual extinction changes corresponding to the photon-dominated envelope, the strongly self-shielded interior, and the cold, dense volumes of the clouds. Within the strongly self-shielded interior of the Orion A cloud, the 13CO abundance varies by 100 per cent with a peak value located near regions of enhanced star formation activity. The effect of CO depletion on to the ice mantles of dust grains is limited to regions with Av > 10 mag and gas temperatures less than ∼20 K as predicted by chemical models that consider thermal evaporation to desorb molecules from grain surfaces. Values of the molecular mass of each cloud are independently derived from the distributions of Av and 13CO column densities with a constant 13CO-to-H2 abundance over various extinction ranges. Within the strongly self-shielded interior of the cloud (Av> 3 mag), 13CO provides a reliable tracer of H2 mass with the exception of the cold, dense volumes where depletion is important. However, owing to its reduced abundance, 13CO does not trace the H2 mass that resides in the extended cloud envelope, which comprises 40–50 per cent of the molecular mass of each cloud. The implied CO luminosity to mass ratios, M/LCO, are 3.2 and 2.9 for Orion A and Orion B, respectively, which are comparable to the value (2.9), derived from γ-ray observations of the Orion region. Our results emphasize the need to consider local conditions when applying CO observations to derive H2 column densities.